A pebble is dropped freely in a well from its top. It takes $20 s$ for the pebble to reach the water surface in the well. Taking $g = 10 m s^{- 2}$ and speed of sound $= 330 m s^{- 1}$ , find: (i) the depth of water surface from the top, and (ii) the time when echo is heard after the pebble is dropped?

(i) 1000 m, (ii) 26.1 s

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(i) 2000 m, (ii) 27 s

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(i) 200 m, (ii) 26.1 s

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(i) 2000 m, (ii) 26.1 s

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Solution

The correct option is C (i) 2000 m, (ii) 26.1 s
i.
$s = u t + 0.5 a t^{2} = 0 + 0.5 (10) (20)^{2} = 2000 m$
ii.
Time for pebble to fall down, $t_{1} = 20 s$
Time for sound to travel from water surface to top of the well, $t_{2} = H / v = 2000 / 330 = 6.06 s$
Total time for echo to be heard, $t = t_{1} + t_{2} = 20 + 6.1 = 26.1 s$

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A pebble is dropped freely in a well from its top. It takes 20 s for the pebble to reach the water surface in the well. Taking g=10 ms−2 and speed of sound =330 ms−1, find: (i) the depth of water surface from the top, and (ii) the time when echo is heard after the pebble is dropped?

The correct option is C (i) 2000 m, (ii) 26.1 si. s=ut+0.5at2=0+0.5(10)(20)2=2000 mii. Time for pebble to fall down, t1=20 s Time for sound to travel from water surface to top of the well, t2=H/v=2000/330=6.06 sTotal time for echo to be heard, t=t1+t2=20+6.1=26.1 s